Arbitrary polarization-switchable metasurfaces

ABSTRACT

An optical component comprises a metasurface comprising nanoscale elements. The metasurface is configured to receive incident light and to generate optical outputs. The geometries and/or orientations of the nanoscale elements provide a first optical output upon receiving a polarized incident light with a first polarization, and provide a second optical output upon receiving a polarized incident light with a second polarization that is different from the first polarization.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. ProvisionalPatent Application 62/379,186, filed Aug. 24, 2016, which isincorporated herein by reference in its entirety.

STATEMENT OF FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under FA9550-14-1-0389and FA9550-16-1-0156, awarded by the Air Force Office of ScientificResearch. The Government has certain rights in the invention.

BACKGROUND

In human experience, light is characterized by its brightness and color.Light is electromagnetic radiation within a range of wavelengths visibleto humans, where wavelength is interpreted by humans in terms of color.Electromagnetic radiation is a wave-like disturbance that propagatesthrough space. A property of electromagnetic radiation related topropagation is polarization, which is imperceptible to the human eye.Polarization refers to a path along which an electric field of theelectromagnetic radiation oscillates. Linear polarization refers to theelectric field oscillating in a two-dimensional plane around a line asthe electromagnetic radiation propagates along the line. Ellipticalpolarization (including the more specific case of circular polarization)refers to the electromagnetic radiation spiraling in an ellipticalpattern centered around a line along which the electromagnetic radiationpropagates. The ability to generate, manipulate, and measurepolarization is important in diverse areas of science and technology.

SUMMARY

Optical metasurfaces may be used to form flat optics, meaning very thin(e.g., nanoscale, with one or more dimensions less than one micrometer(μm)) optics, which can replace conventional optics (e.g., severalorders of magnitude thicker than nanoscale), can replace combinations ofconventional optics, and can provide functionalities that are notachievable by conventional optics. For example, a metasurface can applya spatially-dependent phase shift (e.g., a time delay) to incidentlight, such that the metasurface can be used to manipulate an opticalwavefront with high flexibility.

Described in the present disclosure are metasurfaces that can bedesigned such that a single metasurface can provide multiplefunctionalities responsive to a polarity of light incident on themetasurface. For example, nanoscale components can be designed torespond differently to orthogonal linear polarizations, allowing forpolarization selectivity. Notably, this allows for design ofmetasurfaces behaving as wholly separate optical elements for each ofany two orthogonal linear polarizations. For example, this allows forthe design of a metasurface that, when illuminated with x-polarizedlight provides a function of a lens and, when illuminated withy-polarized light, provides a function of projection of a holographicimage.

Further, according to embodiments of the present disclosure,metasurfaces may be designed to respond to a first ellipticalpolarization with a first functionality and respond to a secondelliptical or linear polarization with a second functionality.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates an ultra-compact metasurface according toembodiments of the present disclosure.

FIG. 1B illustrates conventional optics.

FIG. 2 illustrates an example of a shape-birefringent element accordingto embodiments of the present disclosure.

FIG. 3A illustrates a test that was performed on a metasurface accordingto an embodiment of the present disclosure.

FIG. 3B presents resulting images from the test illustrated in FIG. 3A.

FIG. 3C is a scanning electron microscope (SEM) image of the metasurfacetested in FIG. 3A.

FIG. 3D is an enlarged oblique view of the image of FIG. 3C.

FIG. 4A illustrates six unit cells for six corresponding split-statemetasurface designs.

FIG. 4B provides a comparison between designed and measured propertiesof the six unit cells of FIG. 4A.

FIG. 4C provides a comparison between designed and measured propertiesof the six unit cells of FIG. 4A.

FIG. 4D provides a comparison between designed and measured propertiesof the six unit cells of FIG. 4A.

DETAILED DESCRIPTION

FIG. 1A illustrates an ultra-compact metasurface that can impart one oftwo arbitrary and independent phase profiles on any set of orthogonalpolarizations (linear or elliptical) depending on which polarization isincident. In other words, a single metasurface can function as twocompletely independent optical elements—such as lenses, prisms, andholograms—depending on a polarization state of the incident light.

FIG. 1B illustrates by way of comparison a setup incorporatingconventional optics to realize the same functionality as the metasurfaceillustrated in FIG. 1A. The complicated setup illustrated in FIG. 1Bcould cost in the thousands of dollars. For example, if it is desired tohave light pass through one of two arbitrary optical elements dependingon which of two orthogonal polarizations is incident, incident lightwould first have to pass through a cascade of a half-wave and aquarter-wave plate (e.g., at least $230 each), oriented so as to converteach of the two polarizations to x and y linearly polarized light. Then,a conventional polarization beam splitting cube (e.g., at least $215)would send light into one of two directions depending on incidentpolarization. Then, the two desired optical elements (e.g., lenses,gratings, holograms, etc.) would each be positioned to act on the light,and a second polarization beam splitting cube (e.g., at least $215)would be included to recombine the light. Altogether, such a setup wouldcost upwards of $1000, not including mounting hardware and the opticalelements. Moreover, if a relative phase between the polarizationchannels is of importance, an implementation with conventional opticalelements could prove challenging.

Referring again to FIG. 1A, a metasurface according to embodiments ofthe present disclosure can miniaturize a complicated opticalfunctionality to a single, ultra-compact optical element fabricated by asingle manufacturing stage using lithography. Additionally,manufacturing is scalable, such that multiple metasurfaces (e.g.,including the metasurface illustrated in FIG. 1A) can be preparedconcurrently at low cost; for example, using extreme ultraviolet (EUV)technology. Moreover, outputs of the two polarization channels of eachmetasurface will be in phase without any special consideration.

As can be seen by the above discussion, metasurfaces designed accordingto embodiments of the present disclosure can provide an optimal platformfor ultra-compact polarization optics.

FIG. 2 illustrates an example of a shape-birefringent element depictedfrom a top view. Polarization-sensitive metasurfaces of the typediscussed above are realized as subwavelength-spaced arrays of suchshape-birefringent elements. Although shown as having an ellipticalcross-section (e.g., dielectric pillars of elliptical cross-section withtwo independently tunable dimensions and an arbitrary rotation angle),more generally each shape-birefringent element has two perpendicularsymmetry axes and imparts unique phase shifts on linear polarizationspolarized along each axis. In other words, each element behaves as alinearly birefringent waveplate, and as such can be described by a Jonesmatrix of the form shown in Equation (1).

$\begin{matrix}{J = {{{R\left( {❘{- \theta}} \right)}\begin{bmatrix}e^{i\;\phi_{x}} & 0 \\0 & e^{i\;\phi_{y}}\end{bmatrix}}{R(\theta)}}} & (1)\end{matrix}$

The shape-birefringent element imposes phase shifts ϕ_(x) and ϕ_(y) onlight linearly polarized along its fast and slow axes, which are rotatedby an angle θ relative to a reference coordinate system. R is a 2×2rotation matrix. The wave-plate-like behavior can be realized with, forexample, plasmonic antennas, liquid crystals, or dielectric pillarsexhibiting mode birefringence (fabricated from, e.g., silicon (Si),gallium arsenide (GaAs), or titanium dioxide (TiO₂)). The cross sectionof the pillars may be, e.g., elliptical or rectangular.

Let the orthogonal polarization states upon which the metasurface shouldimpart independent phase profiles be given by orthogonal Jones vectors

${\overset{\rightarrow}{\lambda}}^{+} = \begin{pmatrix}\lambda_{1}^{+} \\\lambda_{2}^{+}\end{pmatrix}$ and${\overset{\rightarrow}{\lambda}}^{-} = {\begin{pmatrix}\lambda_{1}^{-} \\\lambda_{2}^{-}\end{pmatrix}.}$

An output wavefront corresponding to each input polarization state{{right arrow over (λ)}⁺, {right arrow over (λ)}⁻} should havehomogenous polarization, so a condition is imposed that the metasurfaceshould consistently transform the input polarization states to outputpolarization states {{right arrow over (κ)}⁺, {right arrow over (κ)}⁻}as {right arrow over (λ)}⁺→{right arrow over (κ)}⁺ and {right arrow over(λ)}⁻→{right arrow over (κ)}⁻ over an entire spatial extent of themetasurface.

Suppose it is of interest to design a metasurface imposing arbitraryspatial phase profiles ϕ^(±)(x,y) on the states {right arrow over(λ)}^(±). That is, at each point (x,y) a condition is imposed that ametasurface element with Jones matrix J(x,y) satisfies Equation (2) andEquation (3) simultaneously.

J(x,y){right arrow over (λ)}⁺ =e ^(iϕ) ⁺ ^((x,y)){right arrow over(κ)}⁺  (2)

J(x,y){right arrow over (λ)}⁻ =e ^(iϕ) ⁻ ^((x,y)){right arrow over(κ)}⁻  (3)

Mathematically, the above system is solvable for any choice of {{rightarrow over (κ)}⁺, {right arrow over (κ)}⁻}. However, imposing anadditional condition of a single layer of metasurface elements withlinear structural birefringence, J, constrains the design to the form ofEquation (1). It can be shown that this condition directly implies thatthe output polarization states {{right arrow over (κ)}⁺, {right arrowover (κ)}⁻} are the same states as the input states {{right arrow over(λ)}⁺, {right arrow over (λ)}⁻}, but with flipped handedness, describedmathematically as {right arrow over (κ)}^(±)=({right arrow over(λ)}^(±))*, where (*) denotes a complex conjugate.

Given this knowledge of {{right arrow over (κ)}⁺, {right arrow over(κ)}⁻}, the original system can be recast as shown in Equation (4).

$\begin{matrix}{{{J\left( {x,y} \right)} = {\begin{pmatrix}{e^{i\;{\phi^{+}{({x,y})}}}\left( \lambda_{1}^{+} \right)}^{\times} & {e^{i\;{\phi^{-}{({x,y})}}}\left( \lambda_{1}^{-} \right)}^{*} \\{e^{i\;{\phi^{+}{({x,y})}}}\left( \lambda_{2}^{+} \right)}^{\times} & {e^{i\;{\phi^{-}{({x,y})}}}\left( \lambda_{2}^{-} \right)}^{*}\end{pmatrix}\begin{pmatrix}\lambda_{1}^{+} & \lambda_{1}^{-} \\\lambda_{2}^{+} & \lambda_{2}^{-}\end{pmatrix}^{- 1}}}{{J\left( {x,y} \right)} = {{K\left( {x,y} \right)} ⩓^{- 1}}}} & (4)\end{matrix}$

In Equation (4), Λ is a 2×2 matrix whose columns are the input Jonesvectors {{right arrow over (λ)}⁺, {right arrow over (λ)}⁻}, and K(x,y)is a 2×2 matrix whose columns are the phase-shifted output Jones vectorse^(iϕ) ^(±) ^((x,y)){right arrow over (κ)}^(±)=e^(iϕ) ^(±)^((x,y))({right arrow over (λ)}^(±))*

Imposing a condition of {right arrow over (κ)}^(±)=({right arrow over(λ)}^(±))* guarantees that the Jones matrix J(x,y) at each point (x,y)represents a linearly birefringent waveplate (in the sense of (Equation(1)), whose eigenvectors correspond to the fast and slow optical axesoriented at an angle θ, and whose eigenvalues are {e^(iϕ) ^(x) ,e^(iϕ)^(y) }, where {ϕ_(x),ϕ_(y)} are the phase shifts imparted on lightlinearly polarized along the corresponding axes. An appropriate geometryimplementing these phase shifts can then be located using, for example,finite-difference time-domain (FDTD) simulation. In this way, thegeometry and the angular orientation of an element imposing the desiredphases ϕ± on the set of target polarizations λ^(→)± can be determined ateach point, allowing for the design of a metasurface.

The formalism presented above is general and could well apply to anypart of the electromagnetic spectrum, in reflection or transmission, solong as the individual phase-shifting elements implement a Jones matrixof the form of Equation (1).

Thus, a physical metaelement imparting phases ϕ± on arbitrary orthogonalpolarization polarizations λ^(→)± has a Jones matrix J defined byEquation (4). The orientation and dimensions of an element implementingthis Jones matrix J are determined by the angle of the matrix'sorthogonal linear eigen-polarizations and the characteristic phaseshirts {ϕ_(x),ϕ_(y)} imposed. The result can be understood as aunification of the propagation and geometric phases in a single element.Desired phases can be imparted on any set of orthogonal polarizationstates by modifying an element's shape birefringence and angularorientation simultaneously.

Experimental Demonstration

To demonstrate the arbitrary phase control for polarizations other thanlinear polarizations, a metasurface encoding separate holograms for RCP(right-handed circular polarization) and LCP (left-handed circularpolarization) light is fabricated and tested. The near-field phaseprofiles yielding far-field intensity images of a cartoon cat and acartoon dog are computed using iterative phase retrieval. A metasurfaceincluding noninteracting, elliptical TiO₂ pillars is designed to imposethese phase profiles independently on each circular polarization intransmission.

In some embodiments, a broad range of pillars (with semi-major and minoraxes ranging from 50-300 nm, assuming a height of 600 nm set byfabrication process) is simulated using full-wave FDTD simulations tofind those that would satisfy the phase-shifting properties solved forin Eq. (4). The elements of the metasurfaces are birefringentwaveguide-like pillars fabricated of titanium dioxide (TiO₂). Fabricatedwith a TiO₂ process on glass, the pillars are arranged in a squarelattice with 500 nm nearest-neighbor separation as shown in FIGS. 3C and3D. The metasurface is designed for and tested in the visible spectrumat λ=532 nm. The measured far-field intensity profiles upon illuminationwith each circular polarization match the design images with significantdetail as shown in FIGS. 3A and 3B. It is to be understood that thephase profiles imparted on each circular polarization, and thus theprojected far fields, are not fully independent due to a reliance ongeometric phase alone. In these cases, only sections of the far field(such as individual diffraction orders) may contain independent imagesfor each chirality. Using the disclosed method, the phase profilesimparted on each circular polarization (and, thus, the resulting farfields) can be decoupled.

Using the design strategy discussed above, one metasurface can act astwo completely independent, arbitrarily specifiable optical elementsdepending on the polarization of incident light. To demonstrate thistruly arbitrary phase control, metasurfaces encoding separate hologramsfor right circular polarization (a caricature of a dog) and leftcircular polarization (a caricature of a cat) were designed, fabricatedand tested.

The near-field phase profiles yielding far-field intensity images of thecat and dog caricatures were computed using iterative phase retrieval. Ametasurface of non-interacting, elliptical TiO₂ pillars was designed toimpose these phase profiles independently on each circular polarizationin transmission. A broad range of pillars (with semi-major and minoraxes ranging from about 50 nanometers (nm) to about 300 nm) wassimulated using full-wave FDTD simulations to find those that wouldsatisfy the phase-shifting properties solved for in Equation (4). Thepillars were of substantially uniform height (about 600 nm) and werearranged on a square lattice with about 500 nm nearest-neighborseparation. The metasurface was designed for and tested in the visiblespectrum at λ=532 nm.

FIG. 3A illustrates conceptually a test that was performed on themetasurface encoding the dog and cat caricatures. Illustrated at the topof FIG. 3A is light that is right circularly polarized (at 45 degrees)and applied incident to the designed metasurface, where the light passesthrough the elements of the metasurface and is projected as the dogcaricature according to the design. Illustrated at the bottom of FIG. 3Ais light that is left circularly polarized (at 135 degrees) and appliedincident to the same metasurface, where the light passes through theelements of the metasurface and is projected as the cat caricatureaccording to the design.

FIG. 3B provides resulting images from the test illustrated in FIG. 3A.As can be seen, the measured far-field intensity profiles uponillumination with each circular polarization matched the design imageswith significant detail. The bright dot in the center of each imagerepresents zero-order light not coupling into the metasurface due tofabrication imperfections and beam overfilling.

FIG. 3C is a scanning electron microscope (SEM) image of the designed(FIG. 3A) and tested (FIG. 3B) metasurface encoding the dog and catcaricatures. The metasurface is a rectangular array of TiO₂ pillars ofelliptical cross-section and a nearest-neighbor separation of about 500nm. The transverse dimensions of the pillars varied from about 50 nm toabout 300 nm, and each was about 600 nm high.

FIG. 3D is an enlarged, oblique view of the SEM image of FIG. 3D.

Experimental Demonstration

The disclosed technology can be used for optical components such aselliptical polarization beam splitters. The beam splitter operates as ablazed grating defecting light in a direction dependent on thepolarization. The elliptical polarization beam splitters can be used forpolarimetry, where a thorough sampling of polarization state space,including elliptical states, is used to optimize sensitivity.

A metasurface deflecting light at an angle β imposes a linear phaseprofile given by

${\frac{2\;\pi\; x}{\lambda}\sin\;\beta},$

with x being a spatial coordinate along a splitting direction. Ametasurface polarization beam splitter imposes two such phase profileswith different β on each of two polarizations. Using the geometric andpropagation phases in tandem as described above, this is possible forany set of two orthogonal, elliptical polarizations. To illustrate thiscapability, six beam-splitting metasurfaces were designed for sixdifferent sets of elliptical polarizations. The six metasurfaces wereeach designed to deflect orthogonal polarizations at ±7 degrees. It isto be understood that, although equal or opposite angles may bedescribed in the present disclosure by way of convenient example, thetechniques of the present disclosure are not constrained to equal oropposite angles.

FIG. 4A illustrates the design and relative positioning of elements in aunit cell for each of the six selected metasurface designs (where eachof the metasurfaces included multiple of the corresponding unit cells).The design may be used for, e.g., elliptical polarization beamsplitters. In FIG. 4A, the geometry of each beam-splitter unit cell isshown along with the polarization ellipses of the split states. Themetasurfaces were realized with about 600 nm high rectangular TiO₂pillars whose lateral dimensions ranged from about 50 nm to about 250nm, on a hexagonal grid with about 420 nm nearest-neighbor separation.The unit cells shown (#1-6) were tessellated into six metasurfaces, eachabout 300 μm by about 300 μm. Note that unit cell design #1 replaces aconventional geometric phase grating for circular polarizations. Notealso that unit cell designs #2-6 represent new functionality.

The testing of each metasurface beam splitter involved illumination witha set of six test polarization states. By measuring the m=±1 diffractionorder intensity in response to each, the polarization states to whichthe device is most selective can be obtained; ideally, these would matchthe designed split states.

FIG. 4B-4D provide experimental results of the testing of the sixmetasurface designs of FIG. 4A, showing good agreement with the design.The elliptical polarizations chosen (the “split states”) were the sixsets of orthogonal Stokes vectors matching vertices of a regularicosahedron inscribed in a Poincare Sphere. The choice of an icosahedronin particular, and the platonic solids in general, corresponds tooptimal sampling of states for polarimetry.

FIG. 4B shows the northern (right) and southern (left) hemispheres ofthe Poincare sphere, with designed and measured split states formetasurfaces #1-6 plotted, the designed split states of polarization(SOP) being vertices and the measured split SOPs being dots.

FIG. 4C shows in a three-dimensional depiction the information providedin FIG. 4B, where the design SOPs are vertices and the test results aredots.

FIG. 4D presents the information of FIGS. 4B and 4C in bar chart formfor the Stokes coordinates (s₁, s₂, s₃).

Thus has been described a strategy for the design of an ultra-compactoptical element that can effectively function as any two separateoptical elements depending on which of any two orthogonal polarizationstates is incident. The approach was demonstrated in two experiments,namely circular polarization switchable holograms and ellipticalpolarization beam splitters, both at the technologically significantwavelength of λ=532 nm in the visible spectrum. In some embodiments, theapproach can be extended to any frequency range.

Using the disclosed technology, a broad class of metasurfaces can imposearbitrary and independent phase profiles on any set of orthogonalpolarization states, notably extending this capability to chiralpolarizations without relying on chiral birefringence. In particular,the disclosed technology can be used to target elliptical polarizationstates, and provide an intuition for this phenomenon as arising from thecombination of propagation and geometric phase. The formalism of thedisclosed technology generalizes the design space offered bypolarization-sensitive, linearly birefringent metasurfaces, enablingpolarization switchable lenses for chiral polarizations (chiral lenses),more versatile q plates, and improved metasurface polarimeters forpolarization state measurement.

As used herein, the singular terms “a,” “an,” and “the” may includeplural referents unless the context clearly dictates otherwise.

Spatial descriptions, such as “above,” “below,” “up,” “left,” “right,”“down,” “top,” “bottom,” “vertical,” “horizontal,” “side,” “higher,”“lower,” “upper,” “over,” “under,” and so forth, are indicated withrespect to the orientation shown in the figures unless otherwisespecified. It should be understood that the spatial descriptions usedherein are for purposes of illustration only, and that practicalimplementations of the structures described herein can be spatiallyarranged in any orientation or manner, provided that the merits ofembodiments of this disclosure are not deviated by such arrangement.

As used herein, the terms “approximately,” “substantially,”“substantial” and “about” are used to describe and account for smallvariations. When used in conjunction with an event or circumstance, theterms can refer to instances in which the event or circumstance occursprecisely as well as instances in which the event or circumstance occursto a close approximation. For example, when used in conjunction with anumerical value, the terms can refer to a range of variation less thanor equal to ±10% of that numerical value, such as less than or equal to±5%, less than or equal to ±4%, less than or equal to ±3%, less than orequal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%,less than or equal to ±0.1%, or less than or equal to ±0.05%. Forexample, two numerical values can be deemed to be “substantially” thesame if a difference between the values is less than or equal to ±10% ofan average of the values, such as less than or equal to ±5%, less thanor equal to ±4%, less than or equal to ±3%, less than or equal to ±2%,less than or equal to ±1%, less than or equal to ±0.5%, less than orequal to ±0.1%, or less than or equal to ±0.05%.

Additionally, amounts, ratios, and other numerical values are sometimespresented herein in a range format. It is to be understood that suchrange format is used for convenience and brevity and should beunderstood flexibly to include numerical values explicitly specified aslimits of a range, but also to include all individual numerical valuesor sub-ranges encompassed within that range as if each numerical valueand sub-range is explicitly specified.

While the present disclosure has been described and illustrated withreference to specific embodiments thereof, these descriptions andillustrations do not limit the present disclosure. It should beunderstood by those skilled in the art that various changes may be madeand equivalents may be substituted without departing from the truespirit and scope of the present disclosure as defined by the appendedclaims. The illustrations may not be necessarily drawn to scale. Theremay be distinctions between the artistic renditions in the presentdisclosure and the actual apparatus due to manufacturing processes andtolerances. There may be other embodiments of the present disclosurewhich are not specifically illustrated. The specification and drawingsare to be regarded as illustrative rather than restrictive.Modifications may be made to adapt a particular situation, material,composition of matter, method, or process to the objective, spirit andscope of the present disclosure. All such modifications are intended tobe within the scope of the claims appended hereto. While the methodsdisclosed herein have been described with reference to particularoperations performed in a particular order, it will be understood thatthese operations may be combined, sub-divided, or re-ordered to form anequivalent method without departing from the teachings of the presentdisclosure. Accordingly, unless specifically indicated herein, the orderand grouping of the operations are not limitations of the presentdisclosure.

What is claimed is:
 1. An optical component, comprising: a metasurfacecomprising nanoscale elements configured to receive incident light andto generate optical outputs, wherein geometries or orientations of thenanoscale elements provide a first optical output upon receiving apolarized incident light with a first polarization, and provide a secondoptical output upon receiving a polarized incident light with a secondpolarization that is different from the first polarization.
 2. Theoptical component of claim 1, wherein the first polarization and thesecond polarization are orthogonal to each other.
 3. The opticalcomponent of claim 1, wherein the first polarization is an ellipticalpolarization.
 4. The optical component of claim 1, wherein the secondpolarization is an elliptical polarization.
 5. The optical component ofclaim 1, wherein the first polarization or the second polarization is alinear polarization or a circular polarization.
 6. The optical componentof claim 1, wherein the nanoscale elements comprise linearlybirefringent wave plate elements.
 7. The optical component of claim 1,wherein the nanoscale elements comprise linearly birefringent wave plateelements comprising plasmonic antennas, liquid crystals, or dielectricpillars.
 8. An optical device, comprising: a metasurface comprisingnanoscale elements, geometries or orientations of the nanoscale elementsencoding a plurality of hologram phase profiles corresponding to aplurality of polarizations; wherein upon illuminated by an incidentlight with a first polarization of the plurality of polarizations, themetasurface projects a first image based on a first hologram phaseprofile of the plurality of hologram phase profiles, and wherein uponilluminated by an incident light with a second polarization of theplurality of polarizations, the metasurface projects a second imagebased on a second hologram phase profile of the plurality of hologramphase profiles.
 9. The optical device of claim 8, wherein the firstpolarization is a right-handed circular polarization, and the secondpolarization is a left-handed circular polarization.
 10. The opticaldevice of claim 8, wherein the metasurface is a chiral hologramprojector.
 11. The optical device of claim 8, further comprising: aquarter-wave plate for adjusting a chirality of an incoming polarizedlight.
 12. An optical device, comprising: a metasurface comprisingnanoscale elements, wherein geometries or orientations of the nanoscaleelements are arranged such that the metasurface deflects incident lightin different directions depending on polarization states of the incidentlight.
 13. The optical device of claim 12, wherein the polarizationstates of the incident light comprise elliptical polarization states.14. The optical device of claim 12, wherein the polarization states ofthe incident light comprise elliptical polarization states thatcorrespond to orthogonal Stokes vectors matching vertices of anicosahedron.
 15. The optical device of claim 14, wherein the vertices ofan icosahedron are inscribed in a Poincare sphere.
 16. The opticaldevice of claim 12, wherein the metasurfaces is a polarization beamsplitter.
 17. The optical device of claim 12, wherein the optical deviceis a polarimeter.